VI Domains of holomorphy and pseudoconvexity

Christine Laurent-Thiébaut ()
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Christine Laurent-Thiébaut: Université Joseph Fourier, Institut Fourier

A chapter in Holomorphic Function Theory in Several Variables, 2011, pp 113-145 from Springer

Abstract: Abstract At the end of Chapter I and in Chapter III we met open sets in ℂ n on which any holomorphic function can be extended to a larger open set. The open sets which do not have this property are called domains of holomorphy: in this chapter we study such open sets. We start by giving a characterisation of domains of holomorphy in terms of holomorphic convexity (the Cartan–Thullen theorem). We then introduce the notion of pseudoconvexity in order to get a more analytic characterisation of domains of holomorphy. This requires us to define plurisubharmonic functions. We then prove that every domain of holomorphy is pseudoconvex: the converse, which is known as the Levi problem, is studied in Chapter VII.

Keywords: Harmonic Function; Holomorphic Function; Pseudoconvex Domain; Subharmonic Function; Plurisubharmonic Function (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-030-4_6

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DOI: 10.1007/978-0-85729-030-4_6

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